Hemen Hemen Yamabe Soliton Kabul Eden Riemann Submersiyonlar Üzerine Bazı Notlar

Bu çalışmada total uzayı hemen hemen Yamabe soliton olan Riemann submersiyonlar ele alındı. Burada  ’nin herhangi bir lifinin veya B manifoldunun birer Yamabe soliton veya hemen hemen Yamabe soliton olması için bazı gerekli koşullar verildi. Ayrıca liflerin ve B manifoldunun skalar eğrilikleri hesaplandı ve bunlar arasındaki ilişkiler ortaya koyularak söz konusu solitonun bazı karakterizasyonları (yani daralan, durgun veya genişleyen) elde edildi. Anahtar Kelimeler: Riemann manifold; Riemann submersiyon; Hemen hemen Yamabe soliton.

Some Remarks on Riemannian Submersions Admitting An Almost Yamabe Soliton

In this paper, we study the Riemannian submersions  : M B  whose total manifolds admit an almost Yamabe soliton. Here, we give some necessary conditions for which any fiber of  or B are almost Yamabe soliton or Yamabe soliton. Also, we calculate the scalar curvatures of any fiber and B and using them, we present the relations between the scalar curvatures of them and obtain some characterizations of such a soliton (that is, shrinking, steady or expanding). Keywords: Riemannian manifold; Riemannian submersion; Almost Yamabe soliton.

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Hamilton, R., “The Ricci flow on surfaces”, in Mathematics and General Relativity, Contemporary Mathematics, (71), 237-361, 1988.
Barbosa, E., Ribeiro, E., On conformal solutions of the Yamabe flow, Archiv der Mathematik, (101), 79-89, 2013.
Cao, H.D., Sun, X., Zhang, Y., On the structure of gradient Yamabe solitons, Mathematical Research Letters, (19), 767-774, 2012.
Chen, B.-Y., Deshmukh, S., Yamabe and quasi-Yamabe solitons on Euclidean submanifolds, Mediterranean Journal of Mathematics, (15), 194, 2018.
Deshmukh, S., Chen, B.-Y., A Note on Yamabe solitons, Balkan Journal of Geometry and Its Applications, 23(1), 37-43, 2018.
Ma, L., Miquel, V., Remarks on scalar curvature of Yamabe solitons, Annals of Global Analysis and Geometry, 42, 195-205, 2012.
Neto, B.L., A note on (anti-)self dual quasi Yamabe gradient solitons, Results in Mathematics, 71, 527-533, 2017.
Seko, T., Matea, S., Classification of almost Yamabe solitons in Euclidean spaces, Journal of Geometry and Physics, 136, 97-103, 2019.
Falcitelli, M., Ianus, S., Pastore, A.M., Riemannian submersions and related topics, World Scientific Publishing Co. Pte. Ltd. 2004.
Gray, A., Pseudo-Riemannian almost product manifolds and submersion, Journal of Mathematics and Mechanics, (16), 715–737, 1967.
O'Neill, B., The fundamental equations of a Riemannian submersions, Michigan Mathematical Journal, 13, 459-469, 1966.
Akyol, M.A., Gündüzalp, Y., Hemi-slant submersions from almost product Riemannian manifolds, Gulf Journal of Mathematics, 4(3), 15-27, 2016.
Akyol, M.A., Gündüzalp, Y., Semi-invariant semi-Riemannian submersions, Communications Faculty of Sciences University of Ankara Series A1-Mathematics and Statistics, 67(1), 80-92, 2018.
Eken Meriç, Ş., Kılıç, E., Riemannian submersions whose total manifolds admitting a Ricci soliton, International Journal of Geometric Methods in Modern Physics, 16(12), 1950196 (12 pages), 2019.
Özdemir, F., Sayar, C., Taştan, H.M., Semi-invariant submersions whose total manifolds are locally product Riemannian, Quaestiones Mathematicae, 40(7), 909-926, 2017.
Besse, A.L., Einstein manifolds, Springer-Verlag, Berlin, Heildelberg, New York, 1987.